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Tonelli
Tonelli may refer to: * Tonelli (surname) Arts * ''Tonelli'' (film), a 1943 German film Science * Tonelli's theorem (functional analysis) * Tonelli's theorem * Tonelli–Shanks algorithm * Tonelli–Hobson test See also {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fubini's Theorem
In mathematical analysis, Fubini's theorem characterizes the conditions under which it is possible to compute a double integral by using an iterated integral. It was introduced by Guido Fubini in 1907. The theorem states that if a function is Lebesgue integrable on a rectangle X\times Y, then one can evaluate the double integral as an iterated integral:\, \iint\limits_ f(x,y)\,\text(x,y) = \int_X\left(\int_Y f(x,y)\,\texty\right)\textx=\int_Y\left(\int_X f(x,y) \, \textx \right) \texty. This formula is generally not true for the Riemann integral, but it is true if the function is continuous on the rectangle. In multivariable calculus, this weaker result is sometimes also called Fubini's theorem, although it was already known by Leonhard Euler. Tonelli's theorem, introduced by Leonida Tonelli in 1909, is similar but is applied to a non-negative measurable function rather than to an integrable function over its domain. The Fubini and Tonelli theorems are usually combined and for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tonelli (surname)
Tonelli is an Italian surname. Notable people with this name include the following: * Alessandro Tonelli (born 1992), Italian cyclist * Anna Tonelli (c.1763–1846), Italian portrait painter in the late 17th century and early 18th century. * Annalena Tonelli (1943–2003), Italian lawyer and social activist * Bobby Tonelli (born 1975), American actor * Gilles Tonelli (born 1957), Monegasque politician * Giuseppe Tonelli (1668–1732), Italian painter * Guido Tonelli (born 1950), Italian physicist * Ideler Tonelli (1924–2016), Argentine lawyer and politician * John Tonelli (born 1957), Canadian ice hockey player * Leonida Tonelli (1885–1946), Italian mathematician * Lorenzo Tonelli (born 1990), Italian footballer * Maria Valentina Tonelli (1939–2016), Italian writer * Mario Tonelli (1916–2003), American gridiron football player and survivor of the Bataan Death March The Bataan Death March was the Death march, forcible transfer by the Imperial Japanese Army of ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tonelli (film)
''Tonelli'' is a 1943 German drama film directed by Victor Tourjansky and starring Ferdinand Marian, Winnie Markus and Mady Rahl.Bock& Bergfelder p. 346 It was shot at the Bavaria Studios in Munich and at the Deutsches Theater in the city. The film's sets were designed by the art director Ludwig Reiber. It is a circus film, a popular genre in Germany during the war years. Synopsis Circus performer Tonio Tonelli discovers his wife Maja having an affair with his colleague Tino. Tonio goes away, and slowly rebuilds his career before meeting tightrope walker Nelly. The two become a popular sensation, which leads his estranged wife to try and force him back into a partnership with her through blackmail Blackmail is a criminal act of coercion using a threat. As a criminal offense, blackmail is defined in various ways in common law jurisdictions. In the United States, blackmail is generally defined as a crime of information, involving a thr .... When she is found dead, Tonio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tonelli's Theorem (functional Analysis)
In mathematics, Tonelli's theorem in functional analysis is a fundamental result on the weak lower semicontinuity of nonlinear functionals on ''L''''p'' spaces. As such, it has major implications for functional analysis and the calculus of variations. Roughly, it shows that weak lower semicontinuity for integral functionals is equivalent to convexity of the integral kernel. The result is attributed to the Italian mathematician Leonida Tonelli. Statement of the theorem Let \Omega be a bounded domain in n-dimensional Euclidean space \Reals^n and let f : \Reals^m \to \Reals \cup \ be a continuous extended real-valued function. Define a nonlinear functional F on functions u : \Omega \to \Reals^mby F = \int_ f(u(x)) \, \mathrm x. Then F is sequentially weakly lower semicontinuous on the L^p space L^p(\Omega) for 1 < p < +\infty and weakly-∗ lower semicontinuous on |